{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Interference - Mathematical Method Electric fields at point...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Liu UCD Phy9B 07 1 Ch 35. Interference
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Liu UCD Phy9B 07 2 35-1. Interference & Coherence Sources c= λ f
Image of page 2
Liu UCD Phy9B 07 3 Interference Path difference λ /2, 3 λ /2, 5 λ /2… Destructive interference 0, λ, 2λ, 3λ... Constructive interference Coherent Sources: two monochromatic sources of the same frequency & with any definite, constant phase relation (not necessarily in phase). r=2 λ Constructive r=2.5 λ Destructive
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Liu UCD Phy9B 07 4 35-2. Two Source Interference of Light Thomas Young’s experiment (1800) Assumptions: Monochromatic Coherent Path difference r 2 -r 1 =d sin θ Constructive interference (Bright fringes): Destructive interference (Dark fringes): ,... 2 , 1 , 0 ± ± = m λ θ m d = sin λ θ ) 2 1 ( sin + = m d
Image of page 4
Liu UCD Phy9B 07 5 Interference Fringes For small angles only Constructive interference in Young’s Exp: y max =R tan θ m Rsin θ m y max = R m λ /d =0, ±R λ /d, ±2R λ /d, ±3R λ /d… Center is a maximum y min = R( m + 1/2) λ /d = ±R λ /2d, ±3R λ /2d, ±5R λ /2d… Spacing between adjacent maxima /minima: R λ /d (R>>d, R>>y m )
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Liu UCD Phy9B 07 6 35-3. Intensity in Interference Patterns:
Image of page 6
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Mathematical Method Electric fields at point P: E 1 =E cos ( ω t+ φ ) E 2 =E cos t Superposition: E 1 + E 2 =E cos ( t+ )+ E cos t = 2E cos ( φ/2) cos ( t+ φ/2) = Ε P cos ( t+ Amplitude: P = 2E | cos ( φ/2)| Intensity I ∝ E P 2 = 4E 2 cos 2 ( Or: I=I o cos 2 ( Liu UCD Phy9B 07 7 Intensity in Interference Patterns: Phasor Diagram Amplitude: Ε P = 2E | cos ( φ/2)| Intensity I ∝ E P 2 = 4E 2 cos 2 ( φ/2) Or: I=I o cos 2 ( φ/2) Liu UCD Phy9B 07 8 Intensity at y λ π φ 1 2 2 r r − = Phase difference: Intensity: θ sin 2 sin ) ( ) ( 2 1 2 1 2 d kd r r k r r = = − = − = ) sin ( cos 2 cos 2 2 d I I I o o = = Maximum Intensity: or: Small slits ( y<<R, then sin θ = y/R ) m d = sin m d = sin ) ( cos 2 R dy I I o = All peaks have same intensity....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern